On the class of almost (L) limited operators

Oughajji, Fatima Zahra; Fahri, Kamal El; Moussa, Mohammed

doi:10.14232/actasm-020-564-y

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2022

2023

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Cited by 4 publications

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“…The lattice counterpart of this important operator ideal is the class of almost Dunford-Pettis operators: an operator from a Banach lattice to a Banach space is almost Dunford-Pettis if it sends disjoint weakly null sequences to norm null sequences; or, equivalently, if it sends positive disjoint weakly null sequences to norm null sequences. Almost Dunford-Pettis operators have attracted the attention of many experts, for recent developments see [4,5,12,13,18,20,21,22].…”

Section: Introductionmentioning

confidence: 99%

Adjoints and second adjoints of almost Dunford-Pettis operators

Botelho¹,

Garcı́a²

2022

Preprint

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We investigate when the adjoint T * and the second adjoint T * * of an operator T betweeen Banach lattices is almost Dunford-Pettis. First we show when T * * is almost Dunford-Pettis for every T . Then we prove when T * or T * * is almost Dunford-Pettis whenever T is positive and almost Dunford-Pettis. Finally we prove when T * * is an almost Dunford-Pettis operator whenever T is order weakly compact.

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